Question

How much would a bank be willing to loan if the borrower o↵ered terms of repaying $10,000 every three year for 36 years (i.e. first payment 3 years from today, the second payment is received 6 years from today, etc.) and the relevant rate of interest is 7% compounded annually?

(a) $6,620,500
(b) $463,198
(c) $1,489,130
(d) $171,528
(e) $882,928

Answer 1

To calculate the loan amount, we can use the present value of an annuity formula. Using the given values of payment amount, interest rate, and number of payment periods, we find that the loan amount would be $882,928.

Step-by-step explanation:

To calculate the amount that a bank would be willing to loan, we can use the present value of an annuity formula. The formula is:

Loan Amount = Payment Amount * ((1 - (1 + Interest Rate)^-n)) / Interest Rate

In this case, the payment amount is $10,000, the interest rate is 7%, and the number of payment periods is 36. Plugging these values into the formula, we get:

Loan Amount = $10,000 * ((1 - (1 + 0.07)^-36)) / 0.07

After evaluating the expression, we find that the loan amount would be $882,928. Therefore, the correct option is (e) $882,928.